Use our free CBEST Math practice test to review the most important skills and concepts that you must know for this certification exam. Our CBEST math test includes 40 multiple choice practice questions along with detailed explanations. You are not allowed to use a calculator.

Congratulations - you have completed .

You scored %%SCORE%% out of %%TOTAL%%.

Your performance has been rated as %%RATING%%

Your answers are highlighted below.

Question 1 |

### Which of the following is the BEST estimate of 3995 × 102?

450,000 | |

400,000 | |

350,000 | |

300,000 | |

250,000 |

Question 1 Explanation:

The correct answer is (B). The number 3995 is close to 4000, and the number 102 is close to 100. The estimated product can then be written as (4000)(100) = 400,000. (Note that the actual product is 407,490.)

Question 2 |

### Gina buys nine pens at \$1.10 per pen. Which of the following represents the change she would receive if she purchased the pens using a \$20 bill?

\$20 – (9)(\$1.10) | |

(\$20 – 9)(\$1.10) | |

\$20 + (9)(\$1.10) | |

(\$20 – \$1.10)(9) | |

\$20 – 9 – \$1.10 |

Question 2 Explanation:

The correct answer is (A). The cost of the nine pens is (9)(\$1.10). Since Gina paid with a \$20 bill, her change will be the difference between \$20 and the cost of the nine pens. Thus, her change is \$20 – (9)(\$1.10).

Question 3 |

### Each day, Marquis takes two pills of type A medicine, three pills of type B medicine, and one pill of type C medicine. How many pills will he take in 14 days if he forgets to take the type B pills on each of two days?

84 | |

81 | |

78 | |

75 | |

72 |

Question 3 Explanation:

The correct answer is (C). Each day, Marquis is supposed to take a total of six pills. If he takes all of his medication for 14 days, he will take:

(14)(6) = 84 pills

If he forgets to take the three pills of type B on two occasions, this total will reduce by (3)(2) = 6 pills. If he forgets to take his type B pills, he will take:

84 – 6 = 78 pills in 14 days

(14)(6) = 84 pills

If he forgets to take the three pills of type B on two occasions, this total will reduce by (3)(2) = 6 pills. If he forgets to take his type B pills, he will take:

84 – 6 = 78 pills in 14 days

Question 4 |

### Which of these decimals is the greatest?

0.028 | |

0.0082 | |

0.82 | |

0.28 | |

0.8088 |

Question 4 Explanation:

The correct answer is (C). To determine which of these four numbers is greatest, look for the largest digit in the tenths place (the first place to the right of the decimal). Choices (C) and (E) have an “8” in that position, while the other option have either a “2” or a “0.” From this we know that (C) and (E) are greater than the others.

Since they both have an “8” in the tenths place, we need to see which has the greatest number in the hundredths place. Choice (C) has a “2” in the hundredths place while choice (E) has a “0.” Therefore choice (C) is greater.

Since they both have an “8” in the tenths place, we need to see which has the greatest number in the hundredths place. Choice (C) has a “2” in the hundredths place while choice (E) has a “0.” Therefore choice (C) is greater.

Question 5 |

### Three boxes of crayons, identified as Box A, Box B, and Box C, contain the same four colors, as shown in the following chart.

### What percent of all the crayons that are green or brown are contained in Box B?

48% | |

43% | |

40% | |

30% | |

26% |

Question 5 Explanation:

The correct answer is (D). The total number of crayons that are green or brown is 12 + 9 + 2 + 8 + 3 + 6 = 40. In Box B, the number of crayons that are green or brown is 9 + 3 = 12. Thus, percent of green or brown crayons in Box B is:

$\dfrac{12}{40} * 100\% = 30\%$

$\dfrac{12}{40} * 100\% = 30\%$

Question 6 |

### Solve for *x*:

### 3(*x* + 1) = 5(*x* − 2) + 7

−2 | |

2 | |

½ | |

−3 | |

3 |

Question 6 Explanation:

The correct answer is (E). Begin by distributing the 3 and the 5 through their respective parentheses, then combine like terms on each side of the equal sign:

3(

3

3

Add 3 to both sides to maintain the equality:

3

Subtract 3

6 = 2

3 =

Remember that any time a variable is solved for in an equation, the calculated value can be verified by substituting it into the original equation and determining whether it yields a true statement.

3(

*x*+ 1) = 5(*x*− 2) + 73

*x*+ 3 = 5*x*− 10 + 73

*x*+ 3 = 5*x*− 3Add 3 to both sides to maintain the equality:

3

*x*+ 6 = 5*x*Subtract 3

*x*from both sides and then divide the resulting equation by 2 to solve for*x*as follows:6 = 2

*x*3 =

*x*Remember that any time a variable is solved for in an equation, the calculated value can be verified by substituting it into the original equation and determining whether it yields a true statement.

Question 7 |

### Susan, Gus, Harold, and Jeff were left an inheritance by their grandfather. If Susan receives one-eighth of the inheritance, Gus receives one quarter of the inheritance, Harold receives three-eighths of the inheritance, and Jeff receives the remainder, what fraction of the inheritance does Jeff receive?

$\dfrac{1}{4}$ | |

$\dfrac{5}{16}$ | |

$\dfrac{3}{8}$ | |

$\dfrac{3}{4}$ | |

$\dfrac{1}{3}$ |

Question 7 Explanation:

The correct answer is (A). We can add up the fractions received by Susan, Gus, and Harold as follows:

$\dfrac{1}{8} + \dfrac{1}{4} + \dfrac{3}{8}$

$= \dfrac{1}{8} + \dfrac{2}{8} + \dfrac{3}{8}$

$= \dfrac{6}{8} = \dfrac{3}{4}$

We can find the fraction Jeff receives by subtracting the sum of the other three fractions from one, since all the fractions must add up to one. Jeff will receive:

$1 - \dfrac{3}{4} = \dfrac{1}{4}$

$\dfrac{1}{8} + \dfrac{1}{4} + \dfrac{3}{8}$

$= \dfrac{1}{8} + \dfrac{2}{8} + \dfrac{3}{8}$

$= \dfrac{6}{8} = \dfrac{3}{4}$

We can find the fraction Jeff receives by subtracting the sum of the other three fractions from one, since all the fractions must add up to one. Jeff will receive:

$1 - \dfrac{3}{4} = \dfrac{1}{4}$

Question 8 |

### A flight began 6,135,000 feet west of Denver and ended 2,851,000 feet east of Denver. Which of the following is the best estimate of the distance traveled by the flight?

9,000,000 feet | |

3,200,000 feet | |

8,900,000 feet | |

9,100,000 feet | |

9,000 feet |

Question 8 Explanation:

The correct answer is (A). Based on the answer choices, it makes good sense to round to the nearest 100,000 feet:

6,135,000 = 6,100,000

2,851,000 = 2,900,000

Adding our estimates together we get:

6,100,000 + 2,900,000 = 9,000,000 feet

6,135,000 = 6,100,000

2,851,000 = 2,900,000

Adding our estimates together we get:

6,100,000 + 2,900,000 = 9,000,000 feet

Question 9 |

### Use the information below to answer the question that follows.

### A business recorded the number of customers who visited the store throughout the week. How many days had a number of visitors greater than the average number of visitors for the entire week?

6 days | |

4 days | |

5 days | |

2 days | |

3 days |

Question 9 Explanation:

The correct answer is (E). To answer the question we need to determine the average number of visitors for the week:

$\frac{13 + 12 + 16 + 19 + 25 + 33 + 22}{7}$ $= \frac{140}{7} = 20$

How many days had more than 20 visitors?

Fri = 25

Sat = 33

Sun = 22

3 days exceeded the 20-visitor average.

$\frac{13 + 12 + 16 + 19 + 25 + 33 + 22}{7}$ $= \frac{140}{7} = 20$

How many days had more than 20 visitors?

Fri = 25

Sat = 33

Sun = 22

3 days exceeded the 20-visitor average.

Question 10 |

### On a map, the length of the road from Town X to Town Y is measured to be 18 inches. On this map, ¼ inch represents an actual distance of 10 miles. What is the actual distance, in miles, from Town X to Town Y along this road?

580 | |

720 | |

960 | |

1140 | |

1296 |

Question 10 Explanation:

The correct answer is (B). Here we are given a ratio: ¼ inch on the map = 10 miles, so 1 inch on the map = 40 miles. If the map-distance between the towns is 18 inches, then the actual distance must be: 18 × 40 = 720 miles

Question 11 |

### Izzy randomly picks out and keeps a marble from a bag that contains 4 red marbles, 7 blue marbles, 9 yellow marbles, and 6 green marbles. Then Abi picks a marble at random from the same bag. If Izzy’s marble is green, what is the probability that Abi’s marble will also be green?

$\dfrac{3}{65}$ | |

$\dfrac{5}{26}$ | |

$\dfrac{3}{13}$ | |

$\dfrac{1}{5}$ | |

$\dfrac{6}{26}$ |

Question 11 Explanation:

The correct answer is (D). Since Izzy keeps her marble, the number of green marbles and the total number of marbles both reduce by 1. So there will be 5 green marbles and 25 total marbles:

Probability = $\dfrac{5}{25} = \dfrac{1}{5}$

Probability = $\dfrac{5}{25} = \dfrac{1}{5}$

Question 12 |

### If Gabriela needed to buy 9 bottles of soda for a party in which 12 people attended, how many bottles of soda will she need to buy for a party in which 8 people are attending?

6 | |

7 | |

8 | |

10 | |

12 |

Question 12 Explanation:

The correct answer is (A). We can set up a proportion to solve:

$\dfrac{9 \text{ bottles}}{12 \text{ people}} = \dfrac{x \text{ bottles}}{\text 8 \text{ people}}$

Cross-multiply to solve a proportion:

(9)(8) = (12)(

72 = 12

6 =

$\dfrac{9 \text{ bottles}}{12 \text{ people}} = \dfrac{x \text{ bottles}}{\text 8 \text{ people}}$

Cross-multiply to solve a proportion:

(9)(8) = (12)(

*x*)72 = 12

*x*6 =

*x*Question 13 |

### Use the information below to answer the question that follows.

### Four employees each put a business card in a bowl.

### After mixing, each employee removes one card from the bowl at random.

### The first employee to remove a card from the bowl does not get his own card.

### Based on the information above, which of the following conclusions can be made with certainty:

It is possible that two employees drew their own cards. | |

No one drew his own card. | |

Exactly one must have drawn his own card. | |

It is possible that three employees drew their own cards. | |

If the first employee drew the third employee's card, then the third employee must have drawn the first employee's card. |

Question 13 Explanation:

The correct answer is (A). Begin by labeling the employees A, B, C, D. Let A be the employee who draws the first card and let B be the employee whose card is drawn by A:

Answer A is certainly possible (employees C and D could draw their own cards).

Answer B could occur, but it is not guaranteed.

Answer C could occur, but it is not guaranteed.

Answer D is impossible.

Answer E could occur, but it is not guaranteed.

Answer A is certainly possible (employees C and D could draw their own cards).

Answer B could occur, but it is not guaranteed.

Answer C could occur, but it is not guaranteed.

Answer D is impossible.

Answer E could occur, but it is not guaranteed.

Question 14 |

### Use the information below to answer the question that follows.

### Heidi owns only three pairs of footwear: (1) a pair of black boots, (2) a pair of brown boots, and (3) a pair of running shoes.

### If snow is forecast on a day Heidi works, she always wears boots.

### Heidi never wears her brown boots if she will be working in the paint department that day.

### If Heidi is not wearing her black boots, but is working in the paint department today, which of the following conclusions can be made?

She is wearing her brown boots. | |

Snow is not forecast for today. | |

She will wear her brown boots tomorrow. | |

Snow is forecast for tomorrow. | |

She no longer owns black boots. |

Question 14 Explanation:

The correct answer is (B).

Since Heidi is working in the paint department today, she definitely will not be wearing her brown boots.

But, we are told that she is not wearing her black boots.

Since she only owns one pair of brown boots and one pair of black boots, she must not be wearing boots.

If she is not wearing boots, then snow must not have been forecast for today, since she always wears boots when snow is forecast.

Since Heidi is working in the paint department today, she definitely will not be wearing her brown boots.

But, we are told that she is not wearing her black boots.

Since she only owns one pair of brown boots and one pair of black boots, she must not be wearing boots.

If she is not wearing boots, then snow must not have been forecast for today, since she always wears boots when snow is forecast.

Question 15 |

### Use the information that is given below to answer the question that follows.

### Eric is older than Ross

### Erin is older than Rosanna

### Rosanna is younger than Eric

### Based on the information above, which of the following is a possible arrangement listed from oldest to youngest?

Erin, Rosanna, Eric, Ross | |

Erin, Ross, Rosanna, Eric | |

Ross, Erin, Eric, Rosanna | |

Eric, Ross, Erin, Rosanna | |

Eric, Rosanna, Erin, Ross |

Question 15 Explanation:

The correct answer is (D).

We are given 3 facts:

(i) Eric is older than Ross

(ii) Erin is older than Rosanna

(iii) Rosanna is younger than Eric

Use the process of elimination to determine the correct answer.

A. Erin, Rosanna, Eric, Ross: WRONG, violates (iii)

B. Erin, Ross, Rosanna, Eric: WRONG, violates (iii)

C. Ross, Erin, Eric, Rosanna: WRONG, violates (i)

D. Eric, Ross, Erin, Rosanna: CORRECT

E. Eric, Rosanna, Erin, Ross: WRONG, violates (ii)

We are given 3 facts:

(i) Eric is older than Ross

(ii) Erin is older than Rosanna

(iii) Rosanna is younger than Eric

Use the process of elimination to determine the correct answer.

A. Erin, Rosanna, Eric, Ross: WRONG, violates (iii)

B. Erin, Ross, Rosanna, Eric: WRONG, violates (iii)

C. Ross, Erin, Eric, Rosanna: WRONG, violates (i)

D. Eric, Ross, Erin, Rosanna: CORRECT

E. Eric, Rosanna, Erin, Ross: WRONG, violates (ii)

Question 16 |

### Logan correctly answered 70% of the spelling bee questions. If there were 220 questions total, how many did he answer incorrectly

66 | |

154 | |

82 | |

129 | |

60 |

Question 16 Explanation:

The correct answer is (A). If he got 70% correct, then he must have gotten 30% incorrect. We can translate 30% of of 220 to:

$\dfrac{30}{100} \ast 220 = 66$

$\dfrac{30}{100} \ast 220 = 66$

Question 17 |

### The measurements of Sara’s bedroom window are 2 yards 6 inches wide by 1.5 yards high. What are the dimensions of her bedroom window in inches?

18 x 30 | |

36 × 18 | |

52 x 78 | |

78 x 54 | |

82 x 54 |

Question 17 Explanation:

The correct answer is (D). To convert yards to inches, multiply the number of yards by 36 (there are 36 inches in a yard). So 2 yards 6 inches equals:

(2)(36) + 6 = 78

For the second dimension:

(1.5)(36) = 54

(2)(36) + 6 = 78

For the second dimension:

(1.5)(36) = 54

Question 18 |

### The sum of 7 numbers is greater than 140 and less than 210. Which of the following could be the average (arithmetic mean) of the numbers?

20 | |

30 | |

34 | |

160 | |

26 |

Question 18 Explanation:

The correct answer is (E). The formula for the average of a set of numbers is the sum of the numbers divided by the number of terms:

Avg = 140 ÷ 7

Avg = 20

Avg = 210 ÷ 7

Avg = 30

Therefore, the sum must be between 20 and 30.

Avg = 140 ÷ 7

Avg = 20

Avg = 210 ÷ 7

Avg = 30

Therefore, the sum must be between 20 and 30.

Question 19 |

A teacher creates a final exam with 75 questions and expects it to take 90 minutes to complete. The exam consists of 19 short-answer questions with the remainder of the questions being multiple choice. How much time does the teacher expect his students to spend on each of the multiple choice questions?

### Which single piece of information is necessary to solve the problem above?

the number of multiple choice questions | |

the time the teacher expects each short-answer question to take | |

the percentage of questions that are multiple choice | |

the number of students taking the exam | |

the average time the teacher expects each question on the exam to take |

Question 19 Explanation:

The correct answer is (B). Since there are 75 questions on the exam and 19 of the questions are short-answer, we can determine that there are 56 multiple choice questions.

Let a = average time required for each multiple choice question.

Let b = average time required for each short-answer question.

Since the exam is expected to take a total of 90 minutes:

a(56) + b(19) = 90

If we are given b, the time required for each short-answer question, we can use the above equation to solve for a, the time required for each multiple choice question.

Let a = average time required for each multiple choice question.

Let b = average time required for each short-answer question.

Since the exam is expected to take a total of 90 minutes:

a(56) + b(19) = 90

If we are given b, the time required for each short-answer question, we can use the above equation to solve for a, the time required for each multiple choice question.

Question 20 |

A truck driver leaves the depot at 10:30am and arrives at the destination after averaging 60 miles per hour for the 125 mile trip. He waits at the destination while the truck is unloaded, then drives directly back to the depot following the same route. If the truck averages 50 miles per hour for the return trip, how long did the driver wait at the destination while his truck was being unloaded?

### Which single piece of additional information is required to solve this problem?

The distance from the depot to the destination | |

The time it took to drive from depot to destination | |

The maximum speed the truck travelled on its return trip | |

The time when the truck returned to the depot | |

The time required for the truck to travel from destination to depot |

Question 20 Explanation:

The correct answer is (D). The truck travels 60 mph for 125 miles on the outbound trip:

$\dfrac{60 \text{ miles}}{1 \text{ hour}} = \dfrac{125 \text{ miles}}{x \text{ hours}}$

$\rightarrow x = 2\frac{1}{12} \text{ hours}$ $(2 \text{ hours } 5 \text{ minutes})$

The truck travels 50 mph for 125 miles on the return trip:

$\dfrac{50 \text{ miles}}{1 \text{ hour}} = \dfrac{125 \text{ miles}}{y \text{ hours}}$

$\rightarrow y = 2\frac{1}{2} \text{ hours}$ $(2 \text{ hours } 30 \text{ minutes})$

Total driving time = 2 hours 30 minutes + 2 hours 5 minutes = 4 hours 35 minutes

If we were told when the driver returned to the depot, we could use this information along with the time that he left the depot (10:30 am) to determine the total amount of time he was gone.

For example, let's assume we were told he returned to the depot at 3:30 pm. That would mean he was gone a total of 5 hours.

Of those 5 hours, 4 hours and 35 minutes were spent driving.

That means it must have taken 25 minutes (5 hours − 4 hours 35 minutes) to unload the truck.

$\dfrac{60 \text{ miles}}{1 \text{ hour}} = \dfrac{125 \text{ miles}}{x \text{ hours}}$

$\rightarrow x = 2\frac{1}{12} \text{ hours}$ $(2 \text{ hours } 5 \text{ minutes})$

The truck travels 50 mph for 125 miles on the return trip:

$\dfrac{50 \text{ miles}}{1 \text{ hour}} = \dfrac{125 \text{ miles}}{y \text{ hours}}$

$\rightarrow y = 2\frac{1}{2} \text{ hours}$ $(2 \text{ hours } 30 \text{ minutes})$

Total driving time = 2 hours 30 minutes + 2 hours 5 minutes = 4 hours 35 minutes

If we were told when the driver returned to the depot, we could use this information along with the time that he left the depot (10:30 am) to determine the total amount of time he was gone.

For example, let's assume we were told he returned to the depot at 3:30 pm. That would mean he was gone a total of 5 hours.

Of those 5 hours, 4 hours and 35 minutes were spent driving.

That means it must have taken 25 minutes (5 hours − 4 hours 35 minutes) to unload the truck.

Question 21 |

A carnival game offers 4 different stuffed animal prizes. There are two different animals, an ape and a tiger, and each is offered in a small and large size. There are 48 total prizes in the cabinet. 16 are large and 18 of the small prizes are apes.

### Which of the following can be determined?

The total number of tigers | |

the total number of apes | |

the number of small tigers | |

the number of large tigers | |

the number of large apes |

Question 21 Explanation:

The correct answer is (C). To help us visualize the data, let's construct a table:

If there are 48 total prizes and 16 are large, then 32 (48 − 16) must be small.

If there are 32 small prizes and 18 of the small prizes are apes, then 14 of the small prizes must be tigers.

If there are 48 total prizes and 16 are large, then 32 (48 − 16) must be small.

If there are 32 small prizes and 18 of the small prizes are apes, then 14 of the small prizes must be tigers.

Question 22 |

### Liam earns \$8.00 per hour and worked 40 hours. Charlie earns \$20.00 per hour. How many hours would Charlie need to work to equal Liam’s earnings over 40 hours?

12 | |

16 | |

18 | |

20 | |

100 |

Question 22 Explanation:

The correct answer is (B). Begin by calculating Liam’s total earnings after 40 hours:

40 hours × \$8 per hour = \$320

Next, divide this total by Charlie's hourly rate to find the number of hours Charlie would need to work:

\$320 ÷ \$20 per hour = 16 hours

40 hours × \$8 per hour = \$320

Next, divide this total by Charlie's hourly rate to find the number of hours Charlie would need to work:

\$320 ÷ \$20 per hour = 16 hours

Question 23 |

### Elsa brought home $1\frac{2}{3}$ pizzas that were left over from her office party. The next day her husband at $\frac{5}{12}$ of a pizza and her kids ate $\frac{1}{2}$ of a pizza. How much pizza was left?

$\dfrac{11}{12}$ | |

$\dfrac{5}{6}$ | |

$\dfrac{3}{4}$ | |

$\dfrac{2}{3}$ | |

$\dfrac{7}{12}$ |

Question 23 Explanation:

The correct answer is (C). First convert the mixed fraction to an improper fraction. To do this, multiply the whole number with the denominator, add this to the numerator, and place the resulting value above the original denominator.

$1\dfrac{2}{3} = \dfrac{5}{3}$

Next subtract the amount of pizza that is eaten from this number:

$\dfrac{5}{3} - \dfrac{5}{12} - \dfrac{1}{2}$

To do this subtraction you need to find a common denominator. The lowest common denominator for 3, 12, and 2 is 12, since each of the numbers can be divided evenly into 12. Rewrite the fractions with 12 as the denominator. Then subtract and simplify:

$= \dfrac{20}{12} - \dfrac{5}{12} - \dfrac{6}{12}$

$= \dfrac{9}{12} = \dfrac{3}{4}$

$1\dfrac{2}{3} = \dfrac{5}{3}$

Next subtract the amount of pizza that is eaten from this number:

$\dfrac{5}{3} - \dfrac{5}{12} - \dfrac{1}{2}$

To do this subtraction you need to find a common denominator. The lowest common denominator for 3, 12, and 2 is 12, since each of the numbers can be divided evenly into 12. Rewrite the fractions with 12 as the denominator. Then subtract and simplify:

$= \dfrac{20}{12} - \dfrac{5}{12} - \dfrac{6}{12}$

$= \dfrac{9}{12} = \dfrac{3}{4}$

Question 24 |

### Which of the following would be the best unit of measurement to specify the width of a fingernail?

Centimeter | |

Foot | |

Kilogram | |

Inch | |

Millimeter |

Question 24 Explanation:

The correct answer is (E). When determining the best unit of measurement there is no set rule to follow, you are just looking for something that will result in a 'reasonable' number. Something in the range of 5 to 100 units would normally be a good target. You don't want it to measure less than 1 unit and you don't want it to measure in the thousands of units either. The width of a fingernail is definitely less than an inch and maybe about 1 centimeter, so these are not good options. A millimeter is about the thickness of a credit card, and would therefore be the best option.

Question 25 |

### The shoes Jake wants to buy normally sell for $70. There is a 25% off sale on these shoes. To figure out the sale price of the shoes Jake uses the following expression:

$70 − (0.25 × 70)$ Which of the following methods could Jake also use to determine the sale price?$\frac{25}{200}$ × 70 | |

70 ÷ 0.25 | |

(1 − 0.25) × 70 | |

70 − 25 | |

70 ÷ (1 + 0.25) |

Question 25 Explanation:

The correct answer is (C). Let's start by looking the expression that is given in the question:

70 − (0.25 × 70)

Here we are taking the original amount and subtracting away 25% of the original amount.

If we take away 25% of the original amount, we will be left with 75% of the original amount.

0.75 × 70 would give the same result.

We can rewrite this as:

(1 − 0.25) × 70

70 − (0.25 × 70)

Here we are taking the original amount and subtracting away 25% of the original amount.

If we take away 25% of the original amount, we will be left with 75% of the original amount.

0.75 × 70 would give the same result.

We can rewrite this as:

(1 − 0.25) × 70

Question 26 |

### Jon likes to tip 20% at restaurants. To figure out the tip he should leave for a \$35 meal, he uses the following expression:

$0.20 × 35$ Which of the following expressions could Jon have also used?$\dfrac{35}{10} × 2$ | |

$35 ÷ (1 − 0.20) − 35$ | |

$\dfrac{35 × 100}{20}$ | |

$\dfrac{35 − 20}{2}$ | |

$35 ÷ 4$ |

Question 26 Explanation:

The correct answer is (A). Dividing any number by 10 will give you the value of 10% of the original number.

So, $\frac{35}{10}$ gives us 3.50 which is 10% of 35.

To find 20% of 35, we simply double the value we found for 10%.

Thus, $\frac{35}{10}$ × 2 = 7.00 provides the correct result.

So, $\frac{35}{10}$ gives us 3.50 which is 10% of 35.

To find 20% of 35, we simply double the value we found for 10%.

Thus, $\frac{35}{10}$ × 2 = 7.00 provides the correct result.

Question 27 |

### If a bus travels 360 kilometers in 5 hours, how many kilometers will it travel in 9 hours when driving at the same speed?

72 | |

288 | |

620 | |

648 | |

660 |

Question 27 Explanation:

The correct answer is (D). First calculate the distance the bus travels in 1 hour:

360 km ÷ 5 hours = 72 km per hour

Then multiply this number by the total number of hours traveled:

9 hours × 72 km per hour = 648 km

Notice that the final calculation yields the correct units; this helps to confirm that the calculation is correct.

360 km ÷ 5 hours = 72 km per hour

Then multiply this number by the total number of hours traveled:

9 hours × 72 km per hour = 648 km

Notice that the final calculation yields the correct units; this helps to confirm that the calculation is correct.

Question 28 |

### A vase contains 60 marbles, all of which are red or orange. If the ratio of red marbles to orange ones is 1:5, what is the total number of red marbles in the vase?

8 | |

10 | |

12 | |

15 | |

50 |

Question 28 Explanation:

The correct answer is (B). We know that the ratio is 1:5. This means that for every six marbles one of them is red and five are orange. So $\frac{1}{6}$ of the marbles are red:

$\frac{1}{6}$ × 60 = 10

$\frac{1}{6}$ × 60 = 10

Question 29 |

### Cameron purchased a new hat that was on sale for \$5.40. The original price was \$9.00. What percentage discount was the sale price?

5.4% | |

54.0% | |

40.0% | |

60.0% | |

45.0% |

Question 29 Explanation:

The correct answer is (C). The percentage discount is the reduction in price divided by the original price. The difference between original price and sale price is:

$\$9.00 − \$5.40 = \$3.60$

The percentage discount is this difference divided by the original price:

$\$3.60 ÷ \$9.00 = \dfrac{3.60}{9.00}$ $= \dfrac{360}{900}$ $= \dfrac{40}{100}$ $= 40 \text{ percent}$

$\$9.00 − \$5.40 = \$3.60$

The percentage discount is this difference divided by the original price:

$\$3.60 ÷ \$9.00 = \dfrac{3.60}{9.00}$ $= \dfrac{360}{900}$ $= \dfrac{40}{100}$ $= 40 \text{ percent}$

Question 30 |

### Use the menu below to answer the question that follows.

### Neil ordered the following for his family: two cheeseburgers, one hamburger, two large fries, one small fries, and three small sodas. If the total calories for the order is 3370, what is the missing calorie information on the menu?

1000 | |

400 | |

450 | |

480 | |

900 |

Question 30 Explanation:

The correct answer is (C). Let's begin by totaling the calories for the items we are able to:

Two cheeseburgers = 2 × 530 = 1,060 calories

One hamburger = 430 calories

One small fries = 230 calories

Three small sodas = 3 × 250 = 750 calories

If we subtract each of the known calories from the total calories for the order we will know how many calories came from two large fries:

3,370 − 1,060 − 430 − 230 − 750 = 900

900 calories came from two orders of large fries.

Each order of fries is 450 calories.

Two cheeseburgers = 2 × 530 = 1,060 calories

One hamburger = 430 calories

One small fries = 230 calories

Three small sodas = 3 × 250 = 750 calories

If we subtract each of the known calories from the total calories for the order we will know how many calories came from two large fries:

3,370 − 1,060 − 430 − 230 − 750 = 900

900 calories came from two orders of large fries.

Each order of fries is 450 calories.

Question 31 |

### Use the table below to answer the question that follows.

### If a truck travels from Boston to Albany to Cincinnati to Destin, how many miles will the truck travel in total?

1620 miles | |

2440 miles | |

1390 miles | |

2230 miles | |

1780 miles |

Question 31 Explanation:

The correct answer is (A). Let's determine the distance traveled for each of the three legs of the trip using the provided table:

Boston to Albany = 170 miles

Albany to Cincinnati = 720 miles

Cincinnati to Destin = 730 miles

The total distance = 170 + 720 + 730 = 1620 miles

Boston to Albany = 170 miles

Albany to Cincinnati = 720 miles

Cincinnati to Destin = 730 miles

The total distance = 170 + 720 + 730 = 1620 miles

Question 32 |

### Use the table below to answer the question that follows.

### What percentage of the seven vehicles shown in the table were pickups?

46% | |

5% | |

60% | |

16% | |

54% |

Question 32 Explanation:

The correct answer is (E). To find the percentage of vehicles that were pickups, we need to first divide the total number of pickups sold by the total number of all seven vehicles sold:

$\frac{(750,000 + 500,000 + 450,000)}{3,160,000}$ $= \frac{1,700,000}{3,160,000} =$ 0.538

To convert to a percentage, we need to multiply by 100.

0.538 × 100 = 53.8%

54% is the closest answer.

$\frac{(750,000 + 500,000 + 450,000)}{3,160,000}$ $= \frac{1,700,000}{3,160,000} =$ 0.538

To convert to a percentage, we need to multiply by 100.

0.538 × 100 = 53.8%

54% is the closest answer.

Question 33 |

### A restaurant cooked $3\frac{2}{5}$ pounds of rice before opening, and another $1\frac{4}{7}$ pounds later in the afternoon. What was the total amount that they cooked?

$\dfrac{145}{34} \text { pounds}$ | |

$\dfrac{174}{35} \text { pounds}$ | |

$\dfrac{168}{35} \text { pounds}$ | |

$\dfrac{159}{34} \text { pounds}$ | |

$\dfrac{119}{35} \text { pounds}$ |

Question 33 Explanation:

The correct answer is (B). To add mixed number fractions, first convert them to improper fractions, then find a common denominator and add the numerators, placing them over the common denominator. Reduce the final fraction if necessary.

To convert a mixed fraction to an improper fraction, multiply the whole number with the denominator, add this to the numerator, and place the resulting value above the original denominator.

$3\dfrac{2}{5} = \dfrac{17}{5}$

$1\dfrac{4}{7} = \dfrac{11}{7}$

Now find the lowest common denominator between 5 and 7. Since they are both prime numbers, their lowest common denominator is their product, 35. We can rewrite both fractions:

$\dfrac{17}{5} = \dfrac{119}{35}$

$\dfrac{11}{7} = \dfrac{55}{35}$

Now that the denominators are the same, we can add the numerators:

$\dfrac{119}{35} + \dfrac{55}{35} = \dfrac{119 + 55}{35}$ $= \dfrac{174}{35}$

To convert a mixed fraction to an improper fraction, multiply the whole number with the denominator, add this to the numerator, and place the resulting value above the original denominator.

$3\dfrac{2}{5} = \dfrac{17}{5}$

$1\dfrac{4}{7} = \dfrac{11}{7}$

Now find the lowest common denominator between 5 and 7. Since they are both prime numbers, their lowest common denominator is their product, 35. We can rewrite both fractions:

$\dfrac{17}{5} = \dfrac{119}{35}$

$\dfrac{11}{7} = \dfrac{55}{35}$

Now that the denominators are the same, we can add the numerators:

$\dfrac{119}{35} + \dfrac{55}{35} = \dfrac{119 + 55}{35}$ $= \dfrac{174}{35}$

Question 34 |

### The weight, in pounds, of a truck with its load is given by the equation below where $w$ represents the total weight of the truck and its load, and $q$ represents the quantity of castings it is hauling. In the equation, what does the number 35,000 represent?

$w = 500q + 35,000$The combined weight of the truck and a full load of castings | |

The weight of the truck with no load | |

The weight of each casting | |

The maximum weight of castings that the truck can haul |

Question 34 Explanation:

The correct answer is (B). We are told that $w$ represents the total weight of the truck and its load, and $q$ represents the quantity of castings it is hauling.

If a truck is hauling no castings, $q = 0$.

When $q = 0$, $w = 500(0) + 35,000 = 35,000$.

In other words, the weight of the truck by itself (i.e. hauling no castings) is 35,000 lbs.

If a truck is hauling no castings, $q = 0$.

When $q = 0$, $w = 500(0) + 35,000 = 35,000$.

In other words, the weight of the truck by itself (i.e. hauling no castings) is 35,000 lbs.

Question 35 |

### Kara buys groceries once a week. In the past four visits she has spent \$116.25, \$130.07, \$128.82, and \$109.53. If the individual amounts spent are rounded to the nearest \$10, what is the estimate of Kara's total spending for all four visits?

$480 | |

$484.70 | |

$490 | |

$484.67 | |

$460 |

Question 35 Explanation:

The correct answer is (C). Begin by rounding each of the four amounts to the nearest \$10:

\$116.25 → Closer to \$110 or \$120? → \$120

\$130.07 → Closer to \$130 or \$140? → \$130

\$128.82 → Closer to \$120 or \$130? → \$130

\$109.53 → Closer to \$100 or \$110? → \$110

To find total spending, we sum up our four estimates:

\$120 + \$130 + \$130 + \$110 = \$490

\$116.25 → Closer to \$110 or \$120? → \$120

\$130.07 → Closer to \$130 or \$140? → \$130

\$128.82 → Closer to \$120 or \$130? → \$130

\$109.53 → Closer to \$100 or \$110? → \$110

To find total spending, we sum up our four estimates:

\$120 + \$130 + \$130 + \$110 = \$490

Question 36 |

### Aaron determines that 23 gallons of gas are used by his lawn care business in a typical week. If the gas usage is rounded to the nearest 5 gallons, how many gallons would he expect to use in 12 weeks?

300 gallons | |

320 gallons | |

276 gallons | |

240 gallons | |

287 gallons |

Question 36 Explanation:

The correct answer is (A). First, we need to round 23 gallons to the nearest 5 gallons:

23 → Closer to 20 or 25? → 25

Next, we need to multiply 25 by 12:

$\require{cancel} \dfrac{25 \text{ gallons}}{\cancel{\text{week}}} × 12 \require{cancel} \cancel{\text{weeks}}$ $= 300 \text{ gallons}$

23 → Closer to 20 or 25? → 25

Next, we need to multiply 25 by 12:

$\require{cancel} \dfrac{25 \text{ gallons}}{\cancel{\text{week}}} × 12 \require{cancel} \cancel{\text{weeks}}$ $= 300 \text{ gallons}$

Question 37 |

### Use the information below to answer the question that follows.

### What is the average number of hurricanes affecting the US per decade?

11 | |

13 | |

14 | |

15 | |

18 |

Question 37 Explanation:

The correct answer is (D). To find the average, add up all the numbers, then divide by how many numbers there are:

$\text{Average} =$ $\frac{20 + 14 + 11 + 18 + 14 + 19 + 9}{7}$

$\text{Average} = \frac{105}{7} = 15$

$\text{Average} =$ $\frac{20 + 14 + 11 + 18 + 14 + 19 + 9}{7}$

$\text{Average} = \frac{105}{7} = 15$

Question 38 |

### Use the information below to answer the question that follows.

### This pie chart shows Al’s monthly expenses. If Al spent a total of $1,550 in one month, how much did he spend on clothes in that month?

$77.50 | |

$232.50 | |

$775 | |

$7.75 | |

$1,627.50 |

Question 38 Explanation:

The correct answer is (A). From the pie chart it can be seen that clothing represents 5% of his monthly expenses. Recall that 5% is equivalent to $\frac{5}{100}$ or 0.05:

0.05 × \$1,550 = \$77.50

0.05 × \$1,550 = \$77.50

Question 39 |

### Tina has six 5-gallon containers of iced tea that she needs to distribute into 2-gallon containers. Tina uses the following expression to determine how many 2-gallon containers will be required.

(6 × 5) ÷ 2 Which of the following expressions could Tina have also used?5 ÷ 2 | |

(6 × 2) ÷ 5 | |

$\frac{2}{5}$ × 6 | |

(6 ÷ 5) × 2 | |

$\frac{5}{2}$ × 6 |

Question 39 Explanation:

The correct answer is (E).

Consider Tina's first expression, (6 × 5) ÷ 2. First, she determines the total amount of iced tea:

$6 \require{cancel} \cancel{\text{containers}}$ × $\require{cancel} \dfrac{5 \text{ gallons}}{\cancel{\text{container}}}$ $= 30 \text{ gallons}$

Next, she determines how many 2-gallon containers would be required to hold the same amount:

$30 \require{cancel} \cancel{\text{gallons}}$ × $\require{cancel} \dfrac{1 \text{ container}}{ 2\cancel{\text{gallons}}}$$= 15 \text{ containers}$

An alternate approach would use the expression,

$\dfrac{5}{2} × 6$

First, she determines how many 2-gallon containers are contained within each 5-gallon container:

5 $\require{cancel} \cancel{\text{gallons}}$ × $\require{cancel} \dfrac{1 \text{ container}}{ 2\cancel{\text{gallons}}}$ = $\dfrac{5}{2} \text{ containers}$

$= 2\dfrac{1}{2} \text{ containers}$

So each 5-gallon container will fill $2\frac{1}{2}$ 2-gallon containers. Next, she determines how many 2-gallon containers are required to hold 6 5-gallon containers:

$\require{cancel} \dfrac{\frac{5}{2} \text{ 2-gallon containers}}{\cancel{\text{5-gallon containers}}}$ × $6~ \require{cancel} \cancel{\text{5-gallon containers}}$

$= 15 \text{ 2-gallon containers}$

Consider Tina's first expression, (6 × 5) ÷ 2. First, she determines the total amount of iced tea:

$6 \require{cancel} \cancel{\text{containers}}$ × $\require{cancel} \dfrac{5 \text{ gallons}}{\cancel{\text{container}}}$ $= 30 \text{ gallons}$

Next, she determines how many 2-gallon containers would be required to hold the same amount:

$30 \require{cancel} \cancel{\text{gallons}}$ × $\require{cancel} \dfrac{1 \text{ container}}{ 2\cancel{\text{gallons}}}$$= 15 \text{ containers}$

An alternate approach would use the expression,

$\dfrac{5}{2} × 6$

First, she determines how many 2-gallon containers are contained within each 5-gallon container:

5 $\require{cancel} \cancel{\text{gallons}}$ × $\require{cancel} \dfrac{1 \text{ container}}{ 2\cancel{\text{gallons}}}$ = $\dfrac{5}{2} \text{ containers}$

$= 2\dfrac{1}{2} \text{ containers}$

So each 5-gallon container will fill $2\frac{1}{2}$ 2-gallon containers. Next, she determines how many 2-gallon containers are required to hold 6 5-gallon containers:

$\require{cancel} \dfrac{\frac{5}{2} \text{ 2-gallon containers}}{\cancel{\text{5-gallon containers}}}$ × $6~ \require{cancel} \cancel{\text{5-gallon containers}}$

$= 15 \text{ 2-gallon containers}$

Question 40 |

### Use the diagram below to answer the question that follows.

### What is the distance traveled when completing one lap around the track?

2900 meters | |

4700 meters | |

2200 meters | |

2000 meters | |

3400 meters |

Question 40 Explanation:

The correct answer is (E). Each grid space travelled is 100m. The distance travelled in one lap is simply the sum of the grid spaces required to make one lap of the circuit.

As you count around the race track you should end up at 34. Giving a total distance of 34 × 100m = 3400m.

As you count around the race track you should end up at 34. Giving a total distance of 34 × 100m = 3400m.

Once you are finished, click the button below. Any items you have not completed will be marked incorrect.

There are 40 questions to complete.

List |